Inverse Intersections for Boolean Satisfiability Problems

Paul W. Homer

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arXiv · 2501.03281

Inverse Intersections for Boolean Satisfiability Problems

Paul W. Homer

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Abstract

Boolean Satisfiability (SAT) problems are expressed as mathematical formulas. This paper presents a matrix representation for these SAT problems. It shows how to use this matrix representation to get the full set of valid satisfying variable assignments. It proves that this is the set of answers for the given problem and is exponential in size relative to the matrix. It presents a simple algorithm that utilizes the inverse of each clause to find an intersection for the matrix. This gives a satisfying variable assignment.

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Paul W. Homer. 2025-01-05. Inverse Intersections for Boolean Satisfiability Problems. https://arxiv.org/abs/2501.03281

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